Same problem here on one of three Windows 10 computers (no problems on the other 2...) Here's what worked for me.
De-authorize Adobe Digital Editions from the Help command (if not possible, see later. I got an error on this step. Go ahead with the next step anyway)
Uninstall ADE from Control Panel - Programs & Features
Reboot computer
Download and install the latest ADE 4.5 from the official link
http://www.adobe.com/ca/solutions/eb.../download.html
Re-authorize computer
If unable to remove old authorization, or re-authorize, follow these steps from this very helpful link
http://learnbyblogging.com/adobe-dig...ow-i-fixed-it/
1. Quit Adobe Digital Editions.
2. Choose Start > Search for regedit (On Windows 10: it’s in c:\Windows directory)
3. Right click on regedit, ans select “Run as administrator”
4.In the left pane of the Registry Editor, locate the following registry key: HKEY_CURRENT_USER\Software\Adobe\Adept
5. Select “Adept” , right click on it and select “Delete”
6. In the Confirm Key Delete dialog, click OK.
7. Close the Registry Editor.
8. Open Adobe Digital Editions and reauthorize (Help->Authorize Computer…).
And Voila! It worked. I can download epubs again.
Note: I also had to update my version of Overdrive to work for audiobooks.